Temperature compensation for silicon MEMS resonator

ABSTRACT

Thermally induced frequency variations in a micromechanical resonator are actively or passively mitigated by application of a compensating stiffness, or a compressive/tensile strain. Various composition materials may be selected according to their thermal expansion coefficient and used to form resonator components on a substrate. When exposed to temperature variations, the relative expansion of these composition materials creates a compensating stiffness, or a compressive/tensile strain.

BACKGROUND

The present invention relates generally to microelectromechanicalsystems (MEMS). MEMS are devices formed from miniaturized componentsoperatively arranged on a substrate. These components are constructedthrough the use of lithographic and other micro-fabrication technologiesto yield, for example, sensors and actuators.

Many common micromechanical structures are based on the reaction (e.g.,oscillation, deflection or torsion) of a beam structure to an appliedforce. Such beam structures usually have, or are modeled to have, arectangular cross section. However, the degree to which a beam isactually “rectangular” depends on the anisotropy of the etching methodused to form it. Beams are used in the suspension of rigid plates, aslateral oscillators, or as cantilever devices. They are a natural choicefor bearing-less motion detectors. Of particular note, MEMS increasinglyuse beams within resonator structures as part of clock and signalfiltering circuits.

Single crystal semiconductors, such as silicon, are the obvious materialof choice for the fabrication of resonator beams. Such materials haveexcellent mechanical strength and high intrinsic quality factor.Furthermore, the formation and processing of silicon-based materials arewell-developed fields of endeavor drawing upon decades of experiencefrom the integrated circuit industry.

Using polycrystalline silicon (“Poly Si”), for example, one may designresonators having great flexibility in geometry. However, the simple,but commonly used, bending beam and lateral oscillating beam structureswill serve to illustrate not only some of the performance concernsassociated with conventional resonators, but also the precepts of thepresent invention that follow.

Looking at FIG. 1, a bending beam structure is formed by suspending alength of beam 1 having a rectangular cross section above asemiconductor substrate 3 by means of end anchors 5. Typically, anactuating electrode (not shown) is associated with the beam, i.e.,placed in electrostatic field proximity to the beam. The beam is excitedby an electrostatic field induced by the electrode and mechanicallyvibrates in sympathy with oscillations in the electrostatic field.

When a force is applied to the surface of a beam, that surface is saidto be stressed. The average value of this stress, σ, may be expressed asthe loading force, F, divided by the area, A, over which it is applied,or: $\sigma = \frac{F}{A}$

When subjected to a stress, materials literally get pushed (or pulled)out of shape. Strain, σ, is a measure of this deformation, within theelastic limits of the material, and equals the change in length, ΔL,divided by the original length , L_(O), or:$ɛ = \frac{\Delta\quad L}{L_{O}}$

Most materials of interest deform linearly with load. Since load isproportional to stress and deformation is proportional to strain, stressand strain are linearly related. The proportionality constant thatrelates these two measures is known as the elastic modulus or Young'smodulus for the material and is given the symbol “E.” Young's moduli areknown for a great range of materials.

The mechanical stiffness, k_(M), of a beam, as calculated with respectto the oscillation direction parallel to the width of the beam “w,” isproportional to its Young's modulus, E, and certain measures of itsgeometry, including for a beam with a rectangular cross section; length,“L,” and height, “h.” $\begin{matrix}{k_{M} \approx \frac{E \cdot h \cdot w^{3}}{L^{3}}} & {{EQUATION}\quad 1}\end{matrix}$

As is well understood, the Young's modulus for most materials ofinterest changes with temperature according to known thermalcoefficients (αE). For example, Poly Si has a thermal coefficient of 30ppm/K°. Furthermore, the geometry of a beam structure also changes withtemperature, generally expanding with increasing in temperature. Again,as an example, Poly Si has a thermal expansion coefficient, α_(exp), of2.5 ppm/K°.

For some beam designs and related modeling purposes, and given amaterial with an isotropic thermal coefficient, the effect of thermalexpansion on the width of the beam is essentially offset by the effectof thermal expansion on the length of the beam, thus resulting in aremaining linear effect on the height of the beam.

Setting aside electrostatic forces, the resonance frequency (f) of abeam may thus be defined under these assumptions by the equation:$\begin{matrix}{f \approx {\frac{1}{2 \cdot \pi} \cdot \sqrt{\frac{k_{M}}{m_{eff}}}}} & {{EQUATION}\quad 2}\end{matrix}$

where m_(eff) is the effective mass of the beam, constant overtemperature.

Given the critical nature of a beam's resonance frequency to the overallperformance of the resonator, it must remain relatively stable over arange of operating temperatures. In view of the relationship set forthin EQUATION 2, frequency will remain constant only if the mechanicalstiffness remains constant. This, however, will not normally be the caseas thermally induced changes to the Young's modulus tend to change inthe mechanical stiffness of the beam. Accordingly, some externalinfluence is required to “compensate” for the inevitable changes inresonance frequency due to variations in temperature.

Prior attempts have been made to address the issue of resonant beamfrequency stabilization in the presence of changing temperature. See,for example, Wan-Thai Hsu, Stiffness-Compensated Temperature InsensitiveMicromechanical Resonators, MEMS 2002 (-7803-7185-February 2002 IEEE).Such attempts have, however, focused on the issue of verticaloscillation compensation and have prescribing the remedial use of goldor similar materials that are incompatible with CMOS integration.

For other beam designs and related modeling purposes, the frequency (f)of a resonance beam having a rectangular cross section may be expressedby the following equation: $\begin{matrix}{f \approx {\frac{t}{L^{2}}\sqrt{\frac{E}{\rho}}\left( {1 + {\frac{L^{2}}{7t^{2}}S}} \right)}} & {{EQUATION}\quad 3}\end{matrix}$where “p” is the density of the material forming the beam, and “S” is anelastic strain applied to the beam.

As temperature rises, both L and t increase due to thermal expansion,but the effect of the changes in L dominate due to the fact that L ismuch, much greater than t. As a result, the frequency tends to decreaseas temperature increases, and vice versa. Also apparent from theforegoing equation, compressive strain applied to the beam withincreasing temperature will enhance frequency sensitivity as a functionof temperature. Conversely, tensile strain applied to the beam withincreasing temperature will retard frequency sensitivity as a functionof temperature. Such conditions can be better understood by firstassuming a desired relationship wherein the change in frequency, d(f) asa function of the change in temperature, d(T) is equal to 0.Substituting and equating expressions yields: $\begin{matrix}{{\alpha_{\exp}\left( {1 + {\frac{L^{2}}{7t^{2}}S}} \right)} = {\frac{L^{2}}{7t^{2}}\frac{\mathbb{d}S}{\mathbb{d}T}}} & {{EQUATION}\quad 4}\end{matrix}$

For most practical situations, the applied strain, S, will be much, muchless than one. Under such assumptions, the relationship described inEQUATION 4 becomes: $\begin{matrix}{\frac{\mathbb{d}S}{\mathbb{d}T} = {\frac{7t^{2}}{L^{2}}\alpha_{\exp}}} & {{EQUATION}\quad 5}\end{matrix}$

It is again apparent from this relationship that thermally inducedchanges to the resonant frequency of a beam may be retarded (i.e.,compensated for) or enhanced by changes in an elastic strain, (d(S)),applied to the beam.

Unfortunately, the thermal coefficient of Young's modulus for silicon isin the order of 30 ppm/K. This reality leads to considerable temperaturedrift in the frequency of an oscillating beam in the range of 18 ppm/C°.Given nominal requirements for temperature stabilities ranging from 0.1to 50 ppm, and common operating temperature specifications ranging from−40 ° C. to +85 ° C., the putative MEMS designer faces a considerablechallenge in the design of a temperature stable resonator.

Clearly, an efficient compensation mechanism is required for frequencystability of micromechanical resonators over an operating temperaturerange. Such a mechanism should not rely on the incorporation ofmaterials incompatible with CMOS integrations.

SUMMARY OF THE INVENTION

The present invention addresses the issues of temperature compensationfor micromechanical resonators. Both active and passive solutions arepresented. Indeed, employing both active and passive techniques in thesame solution is also presented. Active solutions are characterized bythe application of an external influence on the resonator from a circuitor mechanism external to the resonator structure itself. Passivesolutions draw upon the inherent and disparate thermal expansionqualities found in the semiconductor materials selected to form theresonator structure.

In a first aspect, the present invention provides an active method ofcompensating for thermally induced frequency variations in amicromechanical resonator including an oscillating beam and anelectrode. The method includes determining the actual operatingfrequency for the beam in relation to a desired resonance frequency, andthereafter applying a compensating stiffness to the resonator tomaintain the desired resonance frequency. In one related embodiment, thecompensating stiffness is provided by an electrostatic force applied tothe beam by the electrode.

Within certain active, compensation solutions, the frequency for aresonator may be determined using a feedback circuit that eitherdirectly detects actual operating frequency, or that detects theoperating temperature of the resonator. In response to a correspondingoutput signal from the feedback circuit, a voltage applied to theelectrode may be varied to provide a compensating, electrostaticstiffness on the oscillating beam.

In an alternative set of active, compensation solutions, a working gapbetween the oscillating beam and the electrode is adjusted to vary thecompensating stiffness applied to the beam.

However, other aspects of the present invention are readily applicableto passive approaches to frequency stabilization of a resonator over anoperating temperature range. For example, one method of fabricating amicromechanical resonator according to the present invention forms abeam structure and/or related support structure(s) from a firstmaterial, and the electrode, at least in part, from a second material.Where the first and second materials are properly selected withdisparate thermal expansion coefficients, the relative expansion ofthese components with temperature will tend to passively adjust theworking gap between the beam and electrode to vary a compensatingstiffness applied to the beam, such that resonator frequency remainssubstantially stable over a prescribed temperature range.

There are myriad ways to form an electrode having an effective thermalexpansion coefficient that differs from the substrate, the beam, and/orthe support structures for the beam. Lever arms may be used to magnifythe effects of disparate thermal expansion. In one related embodiment,an electrode and beam are formed from an active layer deposited on asemiconductor substrate. The active layer has a first thermal expansioncoefficient. Thereafter, the body of the electrode is modified toincorporate a second material having a different thermal expansioncoefficient. Within this and similar embodiments, the first and/orsecond materials may be conveniently selected from a group of possiblematerials including; silicon, poly-silicon, Epi-Poly, LPCVD-Poly,silicon dioxide, germanium, silicon-germanium compounds, siliconnitrides, and silicon carbide.

In yet another set of passive compensation solutions, a micromechanicalresonator is formed on a substrate of first material type. Anoscillating beam, related support structure(s), and/or an electrode arethereafter formed from an active layer of second material type. Anchorsfor the support structure(s) and the electrode may be placed atdifferent lateral positions on the substrate, such that relative thermalexpansion of these components on the substrate will tend to adjust aworking gap between the beam and the electrode to thereby compensate forfrequency variations in the beam's oscillations over temperature.

In another closely related aspect, the present invention provides amicromechanical resonator, suspended over a substrate by means of ananchor. At one point, the anchor fixes the beam to the substrate, butthe anchor also includes a composite structure formed from two or morematerials having different thermal expansion coefficients. Where thematerials used to form the anchor are properly selected in relation tothe material used to form the substrate, relative thermal expansionbetween these materials may be used to apply a compressive or tensilestrain on the beam. An appropriate strain upon the beam tends tocompensate for thermally induced frequency variations. Lever arms may beincorporated into a resonator design to amplify the compressive ortensile strain applied to the beam.

BRIEF DESCRIPTION OF THE DRAWINGS

In the course of the detailed description to follow, reference will bemade to the attached drawings. These drawings show different aspects ofthe present invention and, where appropriate, reference numeralsillustrating like structures, components, materials and/or elements indifferent figures are labeled similarly. It is understood that variouscombinations of the structures, components, materials and/or elements,other than those specifically shown, are contemplated and are within thescope of the present invention.

FIG. 1 illustrates a conventional bending beam structure;

FIGS. 2A and 2B are top views of exemplary micromechanical resonatorsincluding a lateral oscillating beam according to the present invention;

FIG. 3 illustrates a extension mechanism adapted to adjust the workinggap shown in FIG. 2 within one exemplary aspect of the presentinvention;

FIGS. 4A, 4B, 5, and 6 illustrate exemplary composite electrodes adaptedfor use with in the context of the present invention;

FIG. 7 illustrates the further incorporation and use of lever arm withinanother exemplary aspect of the present invention;

FIGS. 8 and 9A-C illustrate the use of laterally disposed and compositeanchors within yet other aspects of the present invention;

FIGS. 9D and 9E illustrate cross-sectional views of the embodiment ofFIG. 9C, sectioned along dotted line a-a;

FIG. 10 illustrates a micromechanical resonator adapted to applycompressive or tensile strain upon a beam structure according to stillanother aspect of the present invention; and

FIG. 11 illustrates exemplary embodiment of the present inventionincluding passive and active compensation techniques of FIGS. 3 and 4B.

DETAILED DESCRIPTION

The description that follows presents several design possibilities,methods, and/or mechanical structures in surface micromachining, wherebythermally induced frequency changes in a micromechanical resonator maybe remedied. According to the present invention, semiconductorcompatible materials are highly preferred in the fabrication of suchresonators.

Throughout the description that follows, semiconductor compatiblematerials are presumed in the teaching examples. This materials bias isunderstandable given the contemporary emphasis in CMOS integration ofmicromechanical structures. However, materials incompatible with suchdesigns may also be used, albeit with fewer current design advantages.Compatible materials are not limited to silicon or silicon-basedcompositions, but include all materials capable of being fabricated byconventional integrated circuit techniques and/or integrated upon asemiconductor substrate. As presently preferred, resonators according tothe present invention may be discrete or readily integrated into largerMEMS devices and/or devices including integrated circuits (for example,CMOS circuitry).

In effect, the present invention eliminates the temperature coefficientof the Young's modulus for the material(s) from which a resonator isformed. The term “resonator” encompasses all structures having, orcapable of having, a desired mechanical or electro-mechanical vibration.In the examples that follow, resonators are formed from beam structureshaving presumptively rectangular cross sections. This assumption derivesfrom the obvious fact that explanations drawn to a resonant beam havinga rectangular cross sections are more easily understood thannon-rectangular beam structures. The present invention is not, however,limited to resonant beams having rectangular cross sections.

As discussed above, the frequency of a resonator is known to vary (ordrift) in relation to temperature. Thus, some compensation mechanism isrequired to hold the resonator “on frequency” under the influence of avariable operating temperature. Thermal compensation is preferablyprovided by means of design geometry, rather than process parameters.Furthermore, passive (or inherent) thermal compensation is preferredover active control accomplished by an external circuit. Yet, thepresent invention is also applicable to active thermal compensationsolutions.

Several presently preferred embodiments of the invention are describedbelow. These embodiments are examples teaching the use and making of theinvention. They are, however, only examples and do not fullycircumscribe the bounds of the present invention which is defined by theclaims that follow.

Recall from EQUATION 2 above that the frequency of a resonator, absentthe effect of electrostatic forces, may be defined in relation to itsmechanical stiffness, k_(M). In order to maintain a constant frequency,independent of temperature, it is necessary to compensate for theinevitable variations in the frequency of the resonator.

In one aspect of the present invention, a compensating stiffness isapplied to the resonator to counteract thermally induced frequencychanges. The term “compensating stiffness” broadly denotes any remedialforce applied to the resonator. Unlike mechanical stiffness, whichderives from the internal composition of the resonator, compensatingstiffness results from an external force applied to the physical form ofthe resonator.

For example, an electrostatic force may be used as a compensatingstiffness in the resonator. The electrostatic force, F_(el), between anelectrode and an oscillating beam may be expressed as: $\begin{matrix}{F_{el} = {{\frac{1}{2} \cdot ɛ \cdot \frac{A}{\left( {d - x} \right)^{2}}}U^{2}}} & {{EQUATION}\quad 6}\end{matrix}$where ε is the dielectric constant, A is the area between the beam andelectrode, d is the gap between the beam and the electrode, x is thedeflection due to oscillation, and U is the applied voltage.

Where the deflection due to oscillation is negligible, the compensatingelectrostatic stiffness may be expressed as: $\begin{matrix}{k_{el} = {\frac{\mathbb{d}F_{el}}{\mathbb{d}x} = {{ɛ \cdot A \cdot \frac{1}{d^{3}}}U^{2}}}} & {{EQUATION}\quad 7}\end{matrix}$

Expressed in terms of EQUATION 2 above, the frequency of a resonator asdefined by its mechanical stiffness and an externally appliedelectrostatic stiffness may be expressed as: $\begin{matrix}{f = {\frac{1}{2 \cdot \pi} \cdot \sqrt{\frac{k_{M} - k_{el}}{m}}}} & {{EQUATION}\quad 8}\end{matrix}$

Looking at EQUATIONS 7 and 8, it is apparent that temperature inducedvariations in the mechanical stiffness, and thus the resonancefrequency, may be offset or compensated for by an equal variation in theelectrostatic stiffness. Given fixed values for the dielectric constantand the field area, changes in the compensating electrostatic stiffnessmay be effected by changing the applied voltage U or by changing in theworking gap between the beam and the electrode.

Thus, broadly characterized within an active compensation method, oneaspect of the present invention may be summarized as (1) determining anactual operating frequency for the resonator, and (2) applying, asneeded, a compensating stiffness to the beam, such that a desiredresonance frequency is maintained over an operating temperature range.The step of determining the actual operating temperature may beaccomplished by any one of a number of conventional feedback circuitsdirectly measuring resonator frequency, or indirectly determining theoperating frequency in relation to another measured parameter, such astemperature. In many instances, such data may already exist within thecontemplated use of the resonator and may be advantageously used for thepurpose of resonator temperature compensation.

This concept can be better understood by considering the exampleillustrated in FIGS. 2A and 2B. An oscillating beam 1 is supported inFIG. 2A at opposite ends by support structures 7 and 8 being fixed tosubstrate 3 and having a height of L1. An electrode 2 having height L2is also formed on substrate 3 proximate beam 1 and exerting anelectrostatic force on beam 1 across working gap d (FIGS. 2A and 2B).

It should be noted that the term “height” is an arbitrary designation inrelation to the rectangular example illustrated by the top view shown inFIGS. 2A and 2B, and merely serves to define an axis of orthogonalorientation different from the “length” and “width” of the resonator.

The support structures 7 and 8, electrode 2, and resonator 1 arepreferably all formed from CMOS compatible, silicon-based material.These components may be formed from an active layer deposited on asemiconductor substrate, or from separately deposited layers. The term“deposited” merely describes the placement of an active layer on thesubstrate. It is not process or fabrication technique specific.

Support structures 7 and 8, electrode 2, and beam 1 will expand (andcontract) in accordance with the thermal expansion coefficient for theirmaterial(s) of their composition. For example, support structures 7 and8 are assumed to expand away from the point at which they are fixed tothe substrate, i.e., in the direction of vector 10 shown in FIG. 2.Electrode 2 is assumed to expand in the direction of vector 11. Whilethermal expansion vectors 10 and 11 are shown to be directionallycoincident in the example of FIG. 2, this need not always be the case.However, even where the expansion vectors for these components is in thesame direction, the magnitude of expansion may be controlled by thecareful selection (or alteration) of the composition materials.

Within the context of the working example, the following parameters maybe manipulated during design to achieve temperature compensation duringoperation of the resonator: (a) the ratio between support structureheight L₁ and electrode height L2; (b) the ratio between a (first)thermal expansion coefficient for material used to implement the supportstructures 7 and 8, and a (second) thermal expansion coefficient formaterial used to implement the electrode 2; and, (c) the distance acrossthe working gap. Additionally, the applied voltage U may be varied inrelation to temperature during resonator operation to compensate fortemperature induced changes in frequency. Naturally, different resonatorgeometries will yield different parameters and inter-componentrelationships that may be manipulated to effect thermal frequencycompensation.

In addition to the active compensation solutions discussed, parameters(a) through (c) above may be passively adjusted during operation by, forexample, a careful selection of disparate composition materials used torespectively implement the support structures and the electrode. Theterm “passive” (or passively) as used here refers to a process, method,or adaptation wherein one or more parameters are changed under theinfluence of changes (e.g., thermal expansion) to one or more componentsinternal to the design. Passive adjustments are distinct from “active”adjustments that require the application of an externally derived forceor influence.

Returning to the relationship between frequency, mechanical stiffness,k_(M), and the compensating electrostatic stiffness k_(el) described inEQUATION 8, it is clear that any increase in k_(M) must be matched by anequivalent (or nearly equivalent) increase in k_(el) in order forfrequency f to remain stable. As noted in EQUATION 1, the mechanicalstiffness, k_(M), for a resonator formed from a silicon based materialwill increase in relation to an increase in its Young's modulus, E. Inorder to offset this increase in k_(M), and an increased k_(el) must bederived.

Looking again at EQUATION 7 and assuming a fixed dielectric constant, ε,and field area, A, k_(el) may be increased by increasing the appliedvoltage, U, and/or by reducing the working gap, d, between the resonatorand the electrode. Increasing applied voltage U is a simple, activesolution. A conventional feedback circuit (not shown in FIG. 2) may beimplemented in relation to the resonator. On the basis of a detectedtemperature feedback circuit, applied voltage U may be adjusted tocompensate for any reasonable variance in temperature.

FIG. 2 assumes an electrode 2 fixed to substrate 3. If, however, theelectrode is moveable with respect to beam 1, then the working gap maybe decreased (or increased) in an active, controlled manner using afeedback circuit detecting the temperature or the actual operatingfrequency of the resonator. As shown in FIG. 3, an extension mechanism12, such as a tension spring, a rigid support member, or a thermalactuator (for example, an actuator heating the beam/lever arm structurevia an applied current), may be used to connect electrode 2 withsubstrate 3. The extension mechanism 12 may be electrically ormechanically motivated by an associated actuation driver 14. Using anyone of these exemplary, or similar, mechanisms, the working gap betweenelectrode 2 and beam 1 may be adjusted in response to an increase inoperating temperature, thereby increasing (or decreasing as appropriate)the electrostatic stiffness applied to beam 1 by electrode 2. By carefulcomparison of thermal expansion coefficients and calculation of a rangeof electrostatic stiffness over an expected operating temperature range,one may actively mitigate the effects of temperature change on resonatorfrequency.

Active temperature compensation is attractive in its ability to adaptreal-time to temperature variations. However, active compensationschemes come at the price of some significant additional overhead in theform of actuation drivers and/or extension mechanisms. Thus, in manyapplications a passive temperature compensation solution is desirable.

FIG. 4A illustrates another example of a passive temperaturecompensation. In FIG. 4A, the extension mechanism and/or actuationdriver of FIG. 3 is/are replaced by a pedestal 21 connecting electrode20 to substrate 3. By careful selection of composition material forpedestal 21 and electrode 20, relation to the composition material usedto form support structures 7 and 8, one may adjust the working gapbetween the beam and electrode by the calculated, relative effect ofthermal expansion on materials having different thermal expansioncoefficients.

In similar vein, the example illustrated in FIG. 4B comprises anelectrode 22 formed from two (or more) composition materials 23 and 24having disparate thermal expansion coefficients. The actual choice ofcomposition materials is quite broad, including, as examples,poly-silicon (LPCVD-Poly, Epi-Poly, etc.), single crystalline siliconusing SOI wafers, silicon germanium having multiple Si/Ge ratios,silicon oxides (e.g., SiO₂), silicon nitrides (e.g., Si₃N₄), and siliconcarbide (SiC) of various types.

In the example shown in FIG. 4B, electrode 22 may be formed from aEpiPoly body 23 having been centrally hallowed out, refilled with SiO₂,24, and recapped by EpiPoly. Since SiO₂ has a significantly lowerthermal expansion coefficient (0.5 ppm verses 2.5 ppm for EpiPoly), theintroduction of SiO₂ into the body of electrode 22 will reduce theoverall thermal expansion coefficient of electrode 22. In this example,an outer shell of EpiPoly is required since the electrode must besurface conductive. Given the relative difficulty of forming thick SiO₂layers without cracks, electrode 22 is preferably formed using narrowlyvacated (e.g., etched) trenches subsequently re-filled with SiO₂, or bydepositing multiple layers of SiO₂ within a vacated cavity in theEpiPoly electrode body.

In the related example shown in FIG. 5, a lateral oscillating beam 1 isfixed on either end by respective supports 7 and 8 attached to substrateanchors 7A and 8A. Electrode 28 is fixed to the substrate by anchor 28A.In this example, it is assumed that beam 1, supports 7 and 8, supportanchors 7A and 8A are formed from an EpiPoly layer deposited on thesubstrate. Electrode 28 is also formed from EpiPoly, but portions of theelectrode are vacated (e.g., removed by one or more conventional etchingprocesses), and then refilled with a second material 28B, for exampleSiO₂. Assuming the second material is in fact SiO₂, the resultingelectrode 28 will have a relatively lower thermal expansion coefficientas compared with the components formed from EpiPoly (e.g., the beam,supports, and anchors). Electrode 28 will have a relatively higherthermal expansion coefficient if the second (refill) material wereselected from a group of materials having a thermal expansioncoefficient higher than EpiPoly. For example, germanium has a thermalexpansion coefficient of 4.5 ppm. The grid shaped, vacated portions ofthe electrode work well for SiO₂ refill, but are only one structuralexample of an electrode having a carefully manipulated thermal expansioncoefficient.

FIG. 6 is a cross section view of the resonator structure shown in FIG.5. Where an SiO₂ is the desired refill material, it must be protectedfrom HF-release of the active structure by means of, for example, asilicon nitride layer 30.

The foregoing examples have described electrode structures formed fromat least one additional (secondary) material having a thermal expansioncoefficient different from the thermal expansion coefficient of a(first) primary material forming the other associated components in aresonator structure. However, the present invention also contemplatessimilar alteration of the support structures, the anchors, and/or thebeam in similar manner. It is not necessary that any one of thesecomponents be formed from a combination of materials, refilled orotherwise combined. Rather, materials having disparate thermal expansioncoefficients may be used to form respective components in a resonator.For example, the beam, support structures, and anchors could be formedfrom EpiPoly and the electrode from germanium.

Additionally, the direction and magnitude of relative componentexpansion to effect working gap adjustment may be amplified by the useof one or more lever arms. FIG. 7 illustrates one example of such use. Alever arm 38 is moved to adjust the working gap between electrode 40 andbeam 1. The movement direction of lever arm 38 is controlled by thedifference in thermal expansion (vectors 10 and 11) between a firstsupport 31 and a second support 32, where second support 32 as a fulcrumto lever arm 38. The magnitude of this movement is controlled by thedifference in thermal expansion and by the ratio of length a (a firstlength) and length b (a second length) along the lever arm.

Relative anchor locations on a substrate may also be used to adjust aseparation gap between an electrode and beam. This result may beachieved by considering during the design process the different thermalexpansion coefficients between the substrate and one or more activelayer(s) deposited on the substrate. This approach is illustrated inFIG. 8.

Here, an electrode 29 is separated from beam 1 across a working gap.Electrode 29 is fixed to the substrate at anchor 29A. In contrast,supports 7 and 8 fix beam 1 to the substrate at respective anchors 7Aand 8A. Assuming, as examples, that the substrate is silicon of sapphire(SOS) and the active layer is EpiPoly, the lateral distance L3 betweenthe respective anchors, as measured in the direction of thermalexpansion for the beam, will adjust the working gap over a range ofoperating temperatures.

Relative anchor composition may also be used to effect thermalcompensation for resonance beam frequency variations. Recognizing thatcompressive strain tends to decrease the resonant frequency of a beamand tensile strain tends to increase the resonant frequency, anchorshaving a thermal expansion coefficient different from the substrate maybe used to induce a compressive or tensile strain on the beam. Thisapproach is illustrated in FIGS. 9A and 9B.

Here, a bending (or suspended) beam 1 is supported over substrate 3 byanchors 50 and 52. By forming anchors from two or more materials havingin combination a different thermal expansion coefficient from that ofthe substrate, a compressive or tensile strain may be exerted on beam 1.As above, substrate 3 may be formed from many conventional materialsincluding, without limitation, silicon and germanium.

Anchors 50 and 52 are respectively fixed to substrate 3 at anchor points50A and 52A. The composite anchors may be formed, for example, by SiO₂re-fill into selectively vacated portions of an EpiPoly anchor body.This would result in composite anchors 50 and 52 having a lower overallthermal expansion coefficient with respect to an EpiPoly beam and/or asilicon-based substrate. The length of the composite anchors, L4, asmeasured between an anchor point and the beam, provides leverage for thecompressive or tensile strain applied to beam 1 by the disparate thermalexpansion of the selected materials.

The relative beam composition may also be used to effect thermalcompensation for resonance beam frequency variations. In this regard,with reference to FIGS. 9C and 9D, beam 1 may be comprised of aplurality of materials 1 a and 1 b (for example, silicon, germanium,silicon oxide and/or silicon nitride) that have different thermalexpansion coefficients of expansion. For example, beam 1 may becomprised of an inner-core of silicon and an outer-layer of siliconoxide. Alternatively, beam 1 may be comprised of silicon, germanium andsilicon dioxide (1 a, 1 b, 1 c, respectively—see, FIG. 9E). Indeed, anyof the materials discussed herein (or other materials) may be employedto comprise beam 1.

The invention illustrated in FIG. 9C may also be incorporated with theinventions illustrated in FIGS. 9A and 9B. In this regard, beam 1 may becomprised of a plurality of materials, each having different thermalcoefficients of expansion and anchors 50 and/or 52 are/is comprised oftwo or more materials having in combination a different thermalexpansion coefficient from that of the substrate.

Composite anchors 61 and 62 are combined in FIG. 10 with lever arms 60Aand 60B and compressive/expansion bar 64 to exert a tensile orcompressive force on resonant beam 1. That is, by selecting compositionmaterials having disparate thermal expansion coefficients for anchors 61and 62, compression/expansion bar 64, beam 1, and/or substrate 3, anappropriate compressive or tensile strain may be applied to beam 1 inorder to compensate for temperature induced frequency variations.

Throughout the foregoing disclosure, selected bending beam or lateraloscillating beam structures have been used as examples. However, thefrequency compensation schemes thus illustrated are not limited to theexemplary structures, but have application to all beams useful in MEMs.Further, various materials have been suggested for composition of theexemplary components. Again, these are merely presently preferredexamples. So, long as resonator components are properly designed andfabricated with materials having sufficiently disparate thermalexpansion coefficients, the passive and/or active frequency compensationsolutions taught herein may be achieved.

Moreover, the passive techniques and active techniques described andillustrated herein may also be combined or integrated to provide asolution that employs both passive and active compensation techniques.For example, the embodiments of FIG. 3 and FIG. 4A and/or 4B may beintegrated to provide both a passive and active approach (see, forexample, FIG. 11).

Throughout this application the term “compensation” and “compensate” (orsimilar terms) are used to denote a remedial process by which a majorcomponent or factor of the conditions adversely influencing resonatorstability is addressed and/or ameliorated. Other issues, and even issuesrelating to thermal expansion, such as changes in geometries (forexample, height and/or width) may be less significant in the overallimpact on the compensation. Moreover, the approach herein may be wellsuited to address, compensate for, and/or ameliorate conditionsadversely influencing resonator stability over a finite range oftemperature variations (for example, a predetermined temperature range).

1-31. (canceled)
 32. A microelectromechanical resonator, comprising: asubstrate; an oscillating beam formed from a plurality of materials,wherein the oscillating beam includes: (i) an inner-core comprising afirst material having a first coefficient of thermal expansion, and (ii)an outer-layer, disposed around the inner-core, comprising a secondmaterial having a second coefficient of thermal expansion, wherein thesecond thermal expansion coefficient is different from the first thermalexpansion coefficient; and an anchor, disposed on the substrate andcoupled to the oscillating beam, to, at least in part, support theoscillating beam above the substrate.
 33. The microelectromechanicalresonator of claim 32, wherein the inner-core of the oscillating beamincludes silicon, germanium, silicon oxide or silicon nitride.
 34. Themicroelectromechanical resonator of claim 32, wherein the outer-layer ofthe oscillating beam includes silicon, germanium, silicon oxide orsilicon nitride.
 35. The microelectromechanical resonator of claim 32,wherein the inner-core of the oscillating beam is silicon and theouter-layer of the oscillating beam is silicon oxide.
 36. Themicroelectromechanical resonator of claim 32, wherein the outer-layer isdisposed on the first inner-core.
 37. A microelectromechanicalresonator, comprising: a substrate; an oscillating beam formed from aplurality of materials, wherein the oscillating beam includes: (i) afirst inner-core comprising a first material having a first coefficientof thermal expansion, (ii) a second inner-core, disposed on and aroundthe first inner-core, comprising a second material having a secondcoefficient of thermal expansion, and (iii) an outer-layer, disposed onand around the second inner-core, comprising a third material having athird coefficient of thermal expansion, wherein at least two of thefirst, second and third thermal expansion coefficients are different;and an anchor, disposed on the substrate and coupled to the oscillatingbeam, to, at least in part, support the oscillating beam above thesubstrate.
 38. The microelectromechanical resonator of claim 37, whereinthe first inner-core of the oscillating beam includes silicon,germanium, silicon oxide or silicon nitride.
 39. Themicroelectromechanical resonator of claim 38, wherein the outer-layer ofthe oscillating beam includes silicon, germanium, silicon oxide orsilicon nitride.
 40. The microelectromechanical resonator of claim 37,wherein the first inner-core of the oscillating beam is silicon and theouter-layer of the oscillating beam is silicon oxide.
 41. Themicroelectromechanical resonator of claim 37, wherein the firstinner-core of the oscillating beam is silicon, the second inner-core ofthe oscillating beam is germanium, and the outer-layer of theoscillating beam is silicon oxide.
 42. A micromechanical resonator,comprising: a substrate; an oscillating beam formed from a plurality ofmaterials which, in combination, provide a first thermal expansioncoefficient, wherein the oscillating beam includes: (i) a firstinner-core comprising a first material having a first coefficient ofthermal expansion, and (ii) an outer-layer, disposed around theinner-core, comprising a second material having a second coefficient ofthermal expansion, wherein the second thermal expansion coefficient isdifferent from the first thermal expansion coefficient; and an anchor,disposed on the substrate and coupled to the oscillating beam, to, atleast in part, support the oscillating beam above the substrate, whereinthe anchor is formed from at least one material which provides a thermalexpansion coefficient which is different from the second thermalexpansion coefficient.
 43. The microelectromechanical resonator of claim42, wherein the inner-core of the oscillating beam includes silicon,germanium, silicon oxide or silicon nitride.
 44. Themicroelectromechanical resonator of claim 42, wherein the outer-layer ofthe oscillating beam includes silicon, germanium, silicon oxide orsilicon nitride.
 45. The microelectromechanical resonator of claim 42,wherein the inner-core of the oscillating beam is silicon and theouter-layer of the oscillating beam is silicon oxide.
 45. Themicroelectromechanical resonator of claim 42, wherein the anchor isformed from at least two different materials.
 46. Themicroelectromechanical resonator of claim 42, wherein the anchor isformed from at least three different materials.
 47. Themicroelectromechanical resonator of claim 42, wherein the oscillatingbeam further includes a second inner-core which is disposed on andaround the first inner-core, wherein the second inner-core comprises asecond material having a second coefficient of thermal expansion andwherein at least two of the first, second and third thermal expansioncoefficients are different.
 48. The microelectromechanical resonator ofclaim 47, wherein the first inner-core of the oscillating beam includessilicon, germanium, silicon oxide or silicon nitride.
 49. Themicroelectromechanical resonator of claim 48, wherein the outer-layer ofthe oscillating beam includes silicon, germanium, silicon oxide orsilicon nitride.
 50. The microelectromechanical resonator of claim 47,wherein the first inner-core of the oscillating beam is silicon and theouter-layer of the oscillating beam is silicon oxide.
 51. Themicroelectromechanical resonator of claim 47, wherein the firstinner-core of the oscillating beam is silicon, the second inner-core ofthe oscillating beam is germanium, and the outer-layer of theoscillating beam is silicon oxide.
 52. The microelectromechanicalresonator of claim 47, wherein the anchor is formed from at least twodifferent materials.
 53. The microelectromechanical resonator of claim47, wherein the anchor is formed from at least three differentmaterials.